<p><it>Abstract</it>—In our earlier paper [<ref rid="BIBD11321" type="bib">1</ref>], a textured decomposition based algorithm is developed to solve the optimal routing problem in data networks; a few examples were used to illustrate the speedup advantage and the convergence conditions for the textured algorithm to converge to a global minimum. The speedup advantage is investigated in [<ref rid="BIBD11322" type="bib">2</ref>]. However, the theoretical foundation is not provided. In this paper, we provide the foundation. First, we show that for any textured decomposition, the algorithm always converges to a stationary point, which may not be a global minimum. And then, we prove that if the conditions of the exact convergence theorem are satisfied, the textured algorithm will converge to a global minimum.</p>